Relativistic effects and primordial non-Gaussianity in the galaxy bias

TL;DR

This paper develops a gauge-invariant second-order perturbation theory for galaxy bias, incorporating relativistic effects and primordial non-Gaussianity, revealing their independent and combined impacts on large-scale structure observations.

Contribution

It provides a novel second-order gauge-invariant relation for galaxy bias that includes relativistic effects and primordial non-Gaussianity, with implications for cosmological data analysis.

Findings

Relativistic effects in galaxy bias are independent of primordial non-Gaussianity.

Primordial non-Gaussianity induces scale-dependent and angular modulation in galaxy bias.

The model applies to observationally motivated uniform-redshift gauge.

Abstract

When dealing with observables, one needs to generalize the bias relation between the observed galaxy fluctuation field to the underlying matter distribution in a gauge-invariant way. We provide such relation at second-order in perturbation theory adopting the local Eulerian bias model and starting from the observationally motivated uniform-redshift gauge. Our computation includes the presence of primordial non-Gaussianity. We show that large scale-dependent relativistic effects in the Eulerian bias arise independently from the presence of some primordial non-Gaussianity. Furthermore, the Eulerian bias inherits from the primordial non-Gaussianity not only a scale-dependence, but also a modulation with the angle of observation when sources with different biases are correlated.